U.S. patent number 7,266,044 [Application Number 11/014,457] was granted by the patent office on 2007-09-04 for method and apparatus for acoustic source tracking using a horizontal line array.
This patent grant is currently assigned to United States of America represented by the Secretary of the Navy. Invention is credited to Tsih C. Yang.
United States Patent |
7,266,044 |
Yang |
September 4, 2007 |
Method and apparatus for acoustic source tracking using a
horizontal line array
Abstract
An apparatus for processing passive acoustic signals received on
a horizontal line array that were either emitted from an underwater
object or echo returned from an object, is proposed to track the
motion (bearing change and range change) of an object (target)
relative to the receiver horizontal line array. Adaptive array
processing for a moving object is biased for a moving source when
the number of data samples is limited by the stationariness
condition. Motion compensation can be carried out in the beam
domain by beam shifting for a bearing changing object and frequency
shifting for a range changing object. The method includes receiving
acoustic signals from the target, determining the beam covariance
matrices, determining the target bearing rate and range rate,
processing the beam covariance matrices by compensating for the
target motion, and producing a beam power plot versus time.
Interference signal is suppressed when the interference source does
not have the same motion (bearing and range rate) as the target.
The method does not need detailed environmental acoustic
information of the sound channel normally required to model the
sound propagation.
Inventors: |
Yang; Tsih C. (Great Falls,
VA) |
Assignee: |
United States of America
represented by the Secretary of the Navy (Washington,
DC)
|
Family
ID: |
36595562 |
Appl.
No.: |
11/014,457 |
Filed: |
December 17, 2004 |
Prior Publication Data
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|
|
|
Document
Identifier |
Publication Date |
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US 20060133211 A1 |
Jun 22, 2006 |
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Current U.S.
Class: |
367/124;
367/129 |
Current CPC
Class: |
G01S
3/808 (20130101); G01S 3/86 (20130101); H04R
3/005 (20130101); H04R 2430/20 (20130101) |
Current International
Class: |
G01S
3/86 (20060101) |
Field of
Search: |
;367/119,124,129 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Gershman et al., "Experimental Performance of Adaptive Beamforming
in SOnar Environment with a Towed Array and Moving Interfering
Sources," IEEE Transactions on Signal Processing, vol. 48, No. 1,
Jan. 2000. cited by examiner .
T.C. Yang "Motion compensation for adaptive horizontal line array
processing" J. Acoust. Soc. Am. 113 (1), Jan. 2003 245-260. cited
by other .
T.C. Yang "Beam intensity striations and applications" J. Acoust.
Soc. AM 113 (3), Mar. 2003 1342-1352. cited by other.
|
Primary Examiner: Lobo; Ian J.
Attorney, Agent or Firm: Karasek; John J Koshy; Suresh
Claims
What is claimed is:
1. An apparatus comprising: a horizontal line array comprising a
plurality of hydrophones for receiving a target acoustic signal
from a target and an interference acoustic signal from an
interference source; and a processor cooperating with said
horizontal line array, said processor detecting the target, at
least in art by compensating for at least one of target motion and
interference motion, wherein said target motion comprises at least
one of target bearing and target ranging, and wherein said
interference motion comprises at least one of interference bearing
and interference ranging, said target comprising a target bearing
rate and a target range rate, said interference source comprising
an interference bearing rate and an interference range rate, and
said processor suppressing the interference acoustic signal based
on a difference between at least one of the target bearing rate and
the target range rate, and at least one of the interference bearing
rate and the interference range rate, and wherein said processor
determines a beam covariance matrix for the target from a plurality
of hydrophone covariance matrices corresponding to said plurality
of hydrophones.
2. The apparatus according to claim 1, wherein the beam covariance
matrix includes a target-search sub-space beam covariance matrix
representing a largest beam power of the target, and an
interference sub-space beam covariance matrix representing an
interference contribution from the interference source, said
processor separating the target-search sub-space from the
interference sub-space by suppressing the interference
contribution.
3. The apparatus according to claim 2, said processor shifting the
target-search sub-space beam covariance matrix according to a
plurality of estimated target-hearing rates, thereby generating a
plurality of shifted target-search sub-space beam covariance
matrices; said processor summing the plurality of shifted
target-search sub-space beam covariance matrices; said processor
identifying a largest eigenvalue of a sum of the shifted plurality
of shifted taraet-search sub-space beam covariance matrices; said
processor identifying a calculated target bearing rate from the
largest eigenvalue; said processor shifting the beam covariance
matrix by the calculated target bearing rate; said processor
applying adaptive array processing to the shifted beam covariance
matrix.
4. The apparatus according to claim 2, said processor shifting a
frequency scale of the target-search sub-space beam covariance
matrix according to a plurality of estimated target-range rates,
thereby generating a plurality of shifted target-search sub-space
beam covariance matrices; said processor summing the plurality of
shifted target-search sub-space beam covariance matrices; said
processor identifying a largest eigenvalue of a sum of the shifted
plurality of shifted target-search sub-space beam covariance
matrices; said processor identifying a calculated target range rate
from the largest eigenvalue; said processor shifting the beam
covariance matrix by the calculated target range rate; said
processor applying adaptive array processing to the shifted beam
covariance matrix.
5. The apparatus according to claim 2, said processor shifting the
target-search sub-space beam covariance matrix according to a
plurality of estimated target-bearing rates, thereby generating a
plurality of bearing-rate-shifted target-search sub-space beam
covariance matrices; said processor shifting a frequency scale of
the plurality of bearing-rate-shifted target-search sub-space beam
covariance matrices according to a plurality of estimated
target-range rates, thereby generating a plurality of
bearing-rate-and-range-rate-shifted target-search sub-space beam
covariance matrices; said processor summing the plurality of
bearing-rate-and-range-rate-shifted target-search sub-space beam
covariance matrices; said processor identifying a largest
eigenvalue of a sum of the plurality of
bearing-rate-and-range-rate-shifted target-search sub-space beam
covariance matrices; said processor identifying a calculated target
bearing rate and a calculated target range rate from the largest
eigenvalue; said processor shifting the beam covariance matrix by
the calculated target bearing rate and the calculated target range
rate; said processor applying adaptive array processing to the
shifted beam covariance matrix.
6. A method comprising: receiving, at a horizontal line array
comprising a plurality of hydrophones, a target acoustic signal
from a target and an interference acoustic signal from an
interference source; detecting the target, at least in part, by
compensating for at least one of target motion and interference
motion, wherein the target motion comprises at least one of target
bearing and target ranging, and wherein the interference motion
comprises at least one of interference bearing and interference
ranging, the target comprising a target bearing rate and a target
range rate, the interference source comprising an interference
bearing rate and an interference range rate; supressing the
interference acoustic signal based on a difference between at least
one of the target bearing rate and the target range rate, and at
least one of the interference bearing rate and the interference
range rate; and, determining a beam covariance matrix for the
target from a plurality of hydrophone covariance matrices
corresponding to the plurality of hydrophones.
7. The method according to claim 6, wherein the beam covariance
matrix includes a target-search sub-space beam covariance matrix
representing a largest beam power of the target, and an
interference sub-space beam covariance matrix representing an
interference contribution from the interference source, the method
further comprising separating the target-search sub-space from the
interference sub-space by suppressing the interference
contribution.
8. The method according to claim 7, further comprising: shifting
the target-search sub-space beam covariance matrix according to a
plurality of estimated target-bearing rates, thereby generating a
plurality of shifted target-search sub-space beam covariance
matrices; summing the plurality of shifted target-search sub-space
beam covariance matrices; identifying a largest eigenvalue of a sum
of the shifted plurality of shifted target-search sub-space beam
covariance matrices; identifying a calculated target bearing rate
from the largest eigenvalue; shifting the beam covariance matrix by
the calculated target bearing rate; and applying adaptive array
processing to the shifted beam covariance matrix.
9. The method according to claim 7, further comprising: shifting a
frequency scale of the target-search sub-space beam covariance
matrix according to a plurality of estimated target-range rates,
thereby generating a plurality of shifted target-search sub-space
beam covariance matrices, summing the plurality of shifted
target-search sub-space beam covariance matrices; identifying a
largest eigenvalue of a sum of the shifted plurality of shifted
target-search sub-space beam covariance matrices; identifying a
calculated target range rate from the largest eigenvalue; shifting
the beam covariance matrix by the calculated target range rate; and
applying adaptive array processing to the shifted beam covariance
matrix.
10. The method according to claim 7, further comprising: shifting
the target-search sub-space beam covariance matrix according to a
plurality of estimated target-bearing rates, thereby generating a
plurality of bearing-rate-shifted target-search sub-space beam
covariance matrices, shifting a frequency scale of the plurality of
bearing-rate-shifted target-search sub-space beam covariance
matrices according to a plurality of estimated target-range rates,
thereby generating a plurality of
bearing-rate-and-range-rate-shifted target-search sub-space beam
covariance matrices, summing the plurality of
beaming-rate-and-range-rate-shifted target-search sub-space beam
covariance matrices; identifying a largest eigenvalue of a sum of
the plurality of bearing-rate-and-range-rate-shifted target-search
sub-space beam covariance matrices; identifying a calculated target
bearing rate and a calculated target range rate from the largest
eigenvalue; shifting the beam covariance matrix by the calculated
target hearing rate and the calculated target range rate; and
applying adaptive array processing to the shifted beam covariance
matrix.
Description
TECHNICAL FIELD
This invention relates to a method and apparatus for acoustic
source detection and tracking in bearing and range using a large
aperture horizontal line array, and more particularly, to a method
and apparatus for acoustic source detection and tracking in bearing
and range that suppresses interference signals by accounting for
spatial asymmetry between source motion and interferer motion.
DESCRIPTION OF RELATED ART
Signal processing in underwater acoustics has been centered around
the problem of detection and localization of a target or signal in
an ocean waveguide. Such detection and localization of a low level
acoustic signal (e.g., a quiet target) involves the use of an array
of a large number of hydrophones, which enhances the target
signal-to-noise ("S/N") ratio by the array spatial processing gain.
The array, for example, includes a horizontal aperture to estimate
the signal bearing.
In an ocean environment, particularly in shallow water, many
interference sources, e.g., loud surface ships, are present,
interfering with the detection and directional finding of a target
signal. Interference rejection involves utilization of, for
example, a narrow beam width and an adaptive beamforming algorithm.
A large aperture horizontal array ("HLA") can be used to exclude
many distributed interfering sources (e.g., long range ships)
outside the search beam. High-resolution adaptive beamforming
produces a narrow beam width and suppresses the contribution of
such interfering sources by placing nulls at the interference
bearings (commonly referred to as interference nulling). The larger
the horizontal aperture, the narrower the beam resolution and the
higher the array gain.
Interference suppression is critical to the detection of a weak
signal, lest the signal could be masked by side lobes from the loud
interferences, such as signals from surface ships. This involves,
for example, narrow beams and adaptive array processing. To track
the signal, one needs range estimation, besides bearing
determination. The existing processing techniques have difficulty
in achieving these two goals when the source is moving. In
principle, the larger the horizontal array aperture, the better the
performance in bearing, range estimation and in interference
suppression. However, in practice, source motion severely degrades
the performance as discussed below.
Range estimation is generally described as follows. Standard array
processing assumes that the signal arrives as a plane wave. While
this assumption is widely accepted for radar signal processing, it
is not a good assumption for underwater acoustic signals. The sound
wave in an ocean waveguide encounters reflections from ocean
boundaries (i.e., surface and bottom), refraction by the ocean
medium, which affects the depth dependent sound speed profile, and
scattering by rough boundaries and ocean inhomogeneities. The
signal is a superposition of many curved wave fronts, or
multipaths, arriving at the receivers at different
elevation/depletion angles.
Conventional beamforming uses the concept of delay and sum of
received plane wave signals to estimate the target bearing.
Conventional beamforming does not require detailed environmental
acoustic information, such as the sound speed profile as a function
of depth, the sediment sound speed and attenuation, thickness, etc.
A nominal sound speed of 1500 m/s is often used. Such a
conventional beamforming processor is environment-independent.
However, no range information is available using plane wave
beamforming.
To estimate range, a modification of conventional beamforming has
been proposed assuming a spherical curvature wave front for the
emitted acoustic signal. This is called range-focused beamforming,
as the curvature wave front depends on the source range. To
estimate the target range, range-focused beamforming is applied to
data, assuming several hypothesized target ranges. The beam outputs
with the highest intensities are used to estimate the target range.
Range estimation is limited to a target at near broadside
directions and at ranges less than the Fresnel zone. The
range-focused beamforming approach breaks down at near endfire
directions.
With the advent of matched field/mode/beam processing, it is
possible to extend the detection range by exploiting the multipath
arrivals of low frequency signals using, for example, a large
aperture vertical or horizontal array. Improved signal gain is
obtained because matched field processing matches the data with
signal propagation in the waveguide. Matched field processing may
also be used for source localization. The parameter estimation
aspect of the method has been extensively investigated. Assuming
that the acoustic environment of the ocean is known and that the
signal can be modeled for all source ranges and depth of interest,
the bearing, range, and depth of the target is estimated by the
highest correlation point in the correlation ambiguity function. If
the correlation is in terms of the mode or beam amplitudes of the
replica and data field, one uses matched-mode or matched-beam
processing. This processing requires detailed environmental
acoustic information in order to properly model the signal
propagation in the ocean. Conversely, lack of adequate
environmental information presents a major obstacle in applying
this processing to the real world data. The mismatch between the
model and the real world can result in poor performance, such as
erroneous estimation of the source range. For a moving source,
mismatch can result in large scatters in range estimates, causing
ambiguities and incorrect range tracking. Matching the data at
different ranges demands a higher fidelity in signal propagation
modeling.
Interference rejection is generally described as follows. As
mentioned above, in an ocean environment, particularly in shallow
water, many loud surface ships are present, interfering with the
detection and directional finding of a target signal. Interference
rejection involves, for example, a narrow beam width and a low
sidelobe level. This is accomplished, for example, by using a large
aperture horizontal array ("HLA"), which filters out discrete
interfering sources (e.g., long-range ships) outside the search
beam.
If the objective is to detect a weak source in the background of
high noise or many interfering signals such as that produced by
merchant ships, conventional beamforming for a horizontal line
array is inadequate because of its wide beam width and high
sidelobe levels. A narrow beam is needed to detect a weak signal in
a bearing close to that of an interference signal. If the beam
width is large, a weak signal with a bearing less than the beam
width away from a strong interferer is not detectable. If the
sidelobe level is not sufficiently low, sidelobe leakage from
interfering sources, which can be tens of dB stronger in level than
a target, can easily mask the weak target.
Adaptive array processing is used to overcome the above
shortcomings. A popular algorithm for adaptive array processing is
the minimum variance distortionless response ("MVDR") method. This
method minimizes the array beam outputs in all directions except
the signal direction. It thus yields a low sidelobe level and also
a minimal beam width, both being significantly lower than that of
conventional beamforming.
However, adaptive array processing assumes a plane wave model as in
conventional beamforming. For passive acoustic source detection in
an ocean waveguide, adaptive array processing suffers from a
mismatch between a plane wave signal model and the real signal. For
MVDR, while the sidelobe and noise level are minimized by the
minimum variance method, the signal level is also greatly
diminished by the mismatch between the signal and a plane wave.
This signal mismatch problem is minimized using a white noise
constraint, which adjusts the processor to near conventional output
at the source direction while maintaining minimum variance at other
directions.
Adaptive array processing, such as MVDR, places a null at the
interferer direction and therefore can be used to suppress the
interfering signal. To remove or suppress the interfering signal,
one often uses the eigenvector decomposition method. The strongest
interfering signal can usually be associated with the strongest
eigenvalue obtained by eigenvector decomposition of the covariance
matrix, or the cross-spectral density. Interference suppression can
therefore be achieved by removing these eigenvectors from the
covariance matrix or the weighting factor. This is referred to as
the "dominant mode rejection" method.
The above MVDR methods, as well as other adaptive processing
approaches, assume the existence of a well-conditioned covariance
matrix for the target and interference signals. In practice,
however, the true covariance matrix is not known and must be
estimated from the data. A large number of data samples is normally
required to reduce the variance of the estimated covariance matrix.
When the source and interferers are both stationary, one can
integrate the covariance matrix over a long period of time. When
the target and interference sources are moving, as often is the
case, the non-stationariness of the acoustic environment limits the
number of data samples (i.e., snapshots) available for estimating
the covariance matrix, resulting in a "snapshot-deficient"
condition. Adaptive beam power estimates will be biased under such
a "snapshot-deficient" condition. The performance degradation is
worse as the array aperture increases, thus defeating the purpose
of a large aperture HLA. This is referred to as the source motion
(i.e., degradation) effect on adaptive array processing.
For example, consider a line array of N=100 sensors, with spacing
of 6 m, and thus a total aperture of L=594 m. In data processing,
the fast Fourier transform ("FFT") window must be large enough so
that the signal received on all elements lies within this window.
Thus, .tau..gtoreq.L/c.about.0.4 s, where c=1500 m/s is the nominal
sound speed in water. For a target changing bearing, the
stationariness condition requires that the target stay in the same
beam. If the target changes bearing at a range of 5 km, with a
velocity of 20 knots, the target will stay in a beam of 2.degree.
up to T=R.theta./v=17 sec. For this period of time, the maximum
number of data frames is 17/0.4=43. This number of data frames is
much smaller than the number of sensors (N=100). This is called a
"snapshot-deficient" condition. The MVDR processor will suffer a
severe beam power degradation under the snapshot deficient
condition. When the number of data samples (M) equals the number of
sensors (N), the MVDR beam power suffers a -6 to -12 dB loss for a
line array of 4-16 sensors. If the number of snapshots is three
times the number of sensors (M=3N), the loss is only 1 dB. If the
number of snapshots is less than the number of sensors (M<N),
the loss is expected to be worse than M=N case. The amount of beam
power loss increases with the number of sensors on the array. Thus,
the general rule is that the number of snapshots (i.e., data
frames) should be equal or greater than the number of sensors.
However, in the practical sonar world, this condition is rarely met
for a large aperture horizontal line array when the source or the
interferer is moving.
The dominant mode rejection method mentioned above assumes that the
eigenvectors of the largest eigenvalues are associated with the
interference sources, and that interference suppression can be
achieved by removing these eigenvectors from the covariance matrix
or the weighting factor. The advantage of this method is that it
requires a shorter integration time than the fully adaptive MVDR,
since the large eigenvalues can be estimated using a smaller number
of data samples. Its performance has been studied and compared with
the MVDR method.
If, instead, one uses a large number of data samples to estimate
the covariance matrix, the penalty of ignoring the
non-stationariness condition is described as follows. For moving
sources, the consequence is a spread of the signal energy as
measured by the eigenvalue spectrum of the covariance matrix from
one to more eigenvalues. The price paid is a loss of signal energy
and a reduced ability to reject the interferers. A remedy is to
limit the signal loss using the white noise constraint, but the
performance is severely degraded compared with the stationary
source/interferers case.
The above discussion summarizes two problems in sonar array
processing for a large aperture horizontal line array. One problem
is the non-stationariness due to target/interferer motion, creating
a snapshot deficient condition. The purpose of a large aperture
horizontal line array is to enhance signal detection by
suppressing/rejecting interfering signals through adaptive array
processing. This function is severely limited by the
snapshot-deficient condition. The other problem is lack of
robustness in target range estimation and tracking. At long ranges,
the only processors that offer range estimation are those that do
matched field/mode/beam processing. These processors require
detailed environmental acoustic information to model the signal
propagation in an ocean waveguide. When environmental acoustic
information are lacking or are inaccurate, the results are
erroneous, thereby effectively voiding the use of a large aperture
array for source localization.
SUMMARY OF THE INVENTION
An embodiment of the invention includes an apparatus comprising a
horizontal line array comprising a plurality of hydrophones for
receiving a target acoustic signal from a target and an
interference acoustic signal from an interference source. The
apparatus also includes a processor cooperating with the horizontal
line array, the processor detecting the target, at least in part,
by compensating for target motion and/or interference motion.
Optionally, the target motion comprises target bearing and/or
target ranging, and the interference motion comprises interference
bearing and/or interference ranging. Optionally, the target
comprises a target bearing rate and a target range rate, the
interference source comprises an interference bearing rate and an
interference range rate, and the processor suppresses the
interference acoustic signal based on a difference between the
target bearing rate and/or the target range rate, and the
interference bearing rate and/or the interference range rate.
Optionally, the processor determines a beam covariance matrix for
the target from a plurality of hydrophone covariance matrices
corresponding to the plurality of hydrophones. Optionally, the beam
covariance matrix includes a target-search sub-space beam
covariance matrix representing a largest beam power of the target,
and an interference sub-space beam covariance matrix representing
an interference contribution from the interference source, the
processor separating the target-search sub-space from the
interference sub-space by suppressing the interference
contribution.
Optionally, the processor shifts the target-search sub-space beam
covariance matrix according to a plurality of estimated
target-bearing rates, thereby generating a plurality of shifted
target-search sub-space beam covariance matrices, the processor
summing the plurality of shifted target-search sub-space beam
covariance matrices, the processor identifying a largest eigenvalue
of a sum of the shifted plurality of shifted target-search
sub-space beam covariance matrices, the processor identifying a
calculated target bearing rate from the largest eigenvalue the
processor shifting the beam covariance matrix by the calculated
target bearing rate, the processor applying adaptive array
processing to the shifted beam covariance matrix.
Optionally, the processor shifts a frequency scale of the
target-search sub-space beam covariance matrix according to a
plurality of estimated target-range rates, thereby generating a
plurality of shifted target-search sub-space beam covariance
matrices, the processor summing the plurality of shifted
target-search sub-space beam covariance matrices, the processor
identifying a largest eigenvalue of a sum of the shifted plurality
of shifted target-search sub-space beam covariance matrices, the
processor identifying a calculated target range rate from the
largest eigenvalue, the processor shifting the beam covariance
matrix by the calculated target range rate, the processor applying
adaptive array processing to the shifted beam covariance
matrix.
Optionally, the processor shifts the target-search sub-space beam
covariance matrix according to a plurality of estimated
target-bearing rates, thereby generating a plurality of
bearing-rate-shifted target-search sub-space beam covariance
matrices, the processor shifting a frequency scale of the plurality
of bearing-rate-shifted target-search sub-space beam covariance
matrices according to a plurality of estimated target-range rates,
thereby generating a plurality of
bearing-rate-and-range-rate-shifted target-search sub-space beam
covariance matrices, the processor summing the plurality of
bearing-rate-and-range-rate-shifted target-search sub-space beam
covariance matrices, the processor identifying a largest eigenvalue
of a sum of the plurality of bearing-rate-and-range-rate-shifted
target-search sub-space beam covariance matrices, the processor
identifying a calculated target bearing rate and a calculated
target range rate from the largest eigenvalue, the processor
shifting the beam covariance matrix by the calculated target
bearing rate and the calculated target range rate, the processor
applying adaptive array processing to the shifted beam covariance
matrix.
Optionally, the apparatus also includes a display cooperating with
the processor to display at least one of the target bearing rate
and the target range rate as a function of time.
For example, this invention includes a signal processor that tracks
the source bearing and range, and integrates over the source
motion. This processor is, for example, environment-independent, or
tolerant, and is therefore, for example, insensitive to environment
mismatch as opposed to other range trackers, such as matched field
processing, that require detailed environmental acoustic
information, such as water column sound speed profile and/or bottom
parameters. Coherent time integration of the source motion yields a
temporal processing gain over and above the normal adaptive array
spatial processing gain. Optionally, the motion compensation
algorithm recovers the motion-induced signal power loss suffered by
adaptive array processing such as the MVDR processor carried out in
the element space. When the interferer and target have different
motions, this processor provides additional interference
suppression beyond the normal suppression of a stationary
interference signal provided by adaptive array processing. For
example, the processor is carried out in the beam domain. During
the course of developing an embodiment of the invention, it was
recognized that, in the element domain, the eigenvalues of the
covariance matrix, integrated over a large number of data frames,
are spread into many eigenvalues due to source motion. The target
and interference signal eigenvalues are no longer clearly
separable, as a result, the ability to remove the interference
signal is greatly diminished. During the course of developing an
embodiment of the invention, it was recognized that, in the beam
domain, the target and interference signals at different bearings
often belong to different beam sub-space, and can be integrated
separately by searching for the target bearing and range rate. As a
result, in such an embodiment of the invention, the eigenvalues of
the signal are restored to that equivalent of a stationary source.
The target signal is coherently integrated whereas the interfering
signals are processed incoherently, remaining at a level as before
integration.
Another embodiment of the invention includes a method of
instructing the above-mentioned processor to detect and/or track a
target as described above.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a flowchart of a standard beamforming process in the
phone space.
FIG. 2A is an illustrative graph of a beam pattern.
FIG. 2B is an illustrative beam covariance matrix using
conventional beamforming.
FIG. 3 is an illustrative graph of a true target bearing (solid
curve) versus a hypothesized target bearing (dashed curve) as a
function of time.
FIG. 4A is representation of a beam covariance matrix at time
t.sub.l as a target changes bearing.
FIG. 4B is representation of beam covariance matrices at time
t.sub.i as a target changes bearing.
FIG. 5A is a mathematical representation of beam covariance
matrices summed over data samples for a target changing
bearing.
FIG. 5B is a graph of the eigenvalue spectrum corresponding to FIG.
5A.
FIG. 6 is a flowchart of an embodiment of the invention for
processing a bearing-changing target at a fixed range.
FIG. 7 is a graph of a discrete beam for a target changing bearing,
according to the instant invention.
FIG. 8 is a graph of a processor output, where the peak indicates
the target bearing rate, according to the instant invention.
FIG. 9 is a graph comparing the motion compensated beam power
according to the instant invention to the conventional adaptive
MVDR beam power for a target changing bearing.
FIG. 10 is a mathematical representation of spreading of the
interference beam covariance sub-matrices, when the interference
source has a different bearing rate than the target.
FIG. 11 is a flowchart according to an embodiment of the invention
for processing a target changing range at a fixed bearing.
FIG. 12 is a graph of a processor output, where the peak indicates
the target range rate, according to the instant invention.
FIG. 13 is a graph comparing the motion compensated beam power
according to the instant invention to the conventional adaptive
MVDR beam power for a target changing range.
FIG. 14 is a flowchart according to an embodiment of the invention
for processing a target changing bearing and range at the same
time.
BEST MODE FOR CARRYING OUT THE INVENTION
For motion compensation and/or environment-independent source
tracking, an embodiment of the instant invention, for example,
processes broadband signals in the beam domain. When the signal and
interference field occupy different beams, the motion will spread
the beam covariance eigenvalue spectrum from one to two (or even
three) eigenvalues, but the eigenvalues and eigenvectors of the
signal and interference remain in two separate beam sub-spaces
centered on the signal and interference bearings. For a source
changing bearing, motion effect can be compensated by integrating
over the signal beam covariance matrix (i.e., the beam covariance
sub-matrix in the signal space) that synchronizes with the source
bearing-rate. For a source changing range, elements of the signal
beam covariance matrix have the same range and frequency dependence
as predicted by the wave-guide invariant theory. The source
range-change can be compensated by, for example, frequency-change
(i.e., shift). Using the beam-domain motion compensation algorithm,
adaptive array processing, such as MVDR, yields the same beam power
and beam width for the moving source as the stationary source for
both the bearing and range change cases. Also, the interference
power is suppressed by the motion compensation algorithm when the
interferer has a different motion than the signal source.
Adaptive array beamforming is often based on estimation of the
signal covariance matrix. For example, referring to the standard
beamforming process flowchart of FIG. 1, the conventional MVDR
beamforming algorithm in Step 13 as given by
.function..theta..times..times. ##EQU00001## where
R=<p.sub.datap.sub.data.sup.H> is the covariance matrix
obtained from the received pressure field at a fixed frequency,
obtained after Fourier analysis in Step 11 from the input data in
Step 10; the superscript H denotes Hermition conjugate. The
variable p (without subscript) is the replica field or the steering
vector. The bold face, capital R denotes a matrix, the bold face
lower case p denotes a vector. For plane wave beamforming, the nth
element of the steering vector p is given by
p.sub.n=exp(-jk.sub.0x.sub.n sin .theta.), (2) where .theta. is the
steering vector measured from the broadside of the horizontal line
array (HLA) and k.sub.0 is the wavenumber. For a uniformly
distributed line array, x.sub.n=nd, where d is the phone
spacing.
Conventional beamforming multiplies the pressure field for each
element of the HLA by a phase factor according to a plane wave
arrival at the steered angle,
.alpha..sub.i.ident..alpha.(.theta..sub.i)=.SIGMA..sub.nexp(-jk.sub.0x.su-
b.n sin .theta..sub.i)p.sub.n.ident..SIGMA..sub.nT.sub.inp.sub.n
(3) where k.sub.0 is the wavenumber for sound speed c.sub.0=1500
m/s, .theta..sub.i is the angle of the ith beam and T.sub.in is the
i,n-th element of a matrix T. For a uniformly spaced HLA,
x.sub.n=nd, and T.sub.in=exp(-jk.sub.0dn.kappa..sub.i), where
.kappa..sub.i.ident.sin .theta..sub.i and d is the element spacing.
Assuming that beams are uniformly spaced in the .kappa..sub.i
space, with a total number of beams equaling the number of phones
N, one notes that T is an orthogonal matrix satisfying
TT.sup.H=T.sup.HT=NI. Equation (4) below states that the beam
vector a is an orthogonal transformation of the pressure vector p,
expressed in vector-matrix notion as a=Tp. (4)
In FIG. 1, the beam covariance matrix 14 is then given by
Q=<a.sub.dataa.sub.data.sup.H>=TRT.sup.H, (5) where
a.sub.data is the conventional beam output for the received data,
replacing p by p.sub.data in Eq. (6). The beam space MVDR
algorithm, denoted as MBDR for distinction, is given by
B.sup.MBDR(.theta.)=(a.sup.HQ.sup.-1a).sup.-1 (6) where the beam
steering vector is obtained using Eq. (3) after substituting the
plane wave steering vector p from Eq. (2).
The steering/search angle at the look direction is denoted as
.theta..sub.S, the signal angle (bearing) as .theta..sub.T, and the
beam index used in matrix multiplication as .theta..sub.i. The beam
steering vector a is the conventional beam output for a plane wave
arriving at the angle .theta..sub.S. It has a beam width
sin(.theta..sub.i-.theta..sub.S).apprxeq.1/N, N being the number of
sensors on the HLA, as shown in FIG. 2A. Thus, the elements of the
beam steering vector a are small except for the .+-.w beams
adjacent to the signal-look beam. This is particularly so for a
large aperture HLA, where the sidelobe levels are low. In this
approximation, only the 2w+1 beam sub-space of the beam covariance
matrix, as shown in FIG. 2B, will contribute to the MBDR output at
angle .theta..sub.S. Thus we can use a beam sub-space processor
B.sup.MBDR(.theta.)=(a.sup.H{circumflex over (Q)}.sup.-1a).sup.-1,
(7) where a is a sub-vector of a, of dimension 2w+1, and
{circumflex over (Q)} is a sub-matrix of Q, of dimension
(2w+1).times.(2w+1) indexed around the signal-look directions. The
parameter w denotes the number of signal beams covered by the
signal beam width. For example, if the beam width is 2.degree. and
a beam is formed at each degree, then w=2. For this case, the
matrix inversion will be for a 5.times.5 matrix, which is much
faster than the inversion of a matrix of dimension 100.times.100 in
the element space. Search for Target Bearing Rate for a Fixed
Target Range
An embodiment of the invention including a beam domain motion
compensation algorithm works as follows. From the bearing time
record using, for example, conventional beamforming, a target of
interest can be found. Its approximate bearing and the
corresponding beam sub-space for the target signal are determined.
The processor need not know the exact bearing-rate and will search
for the bearing-rate that yields the highest beam power for the
signal beam sub-space, as determined by the value of its first
eigenvalue. For a given bearing rate, a bearing track is
constructed. As an example, FIG. 3 shows the target bearing track
in the sin .theta. space for an initial bearing of -6.degree. with
a hypothesized bearing rate of 0.12 deg/unit-time. The target
bearing rate is only approximately known from the bearing time
record. The dashed line in FIG. 3 shows a hypothetical bearing
track as part of the search. The target bearing changed by an
amount .DELTA..theta. over a time period of
.DELTA.t=t.sub.i-t.sub.l, yielding a bearing rate
.alpha.=.DELTA..theta./.DELTA.t.
As the target changes bearing, the target beam covariance
sub-matrix Q will be centered at different angles. FIGS. 4A and 4B
show the target beam sub-matrices at t.sub.l and t.sub.i,
respectively, which occupy different beam space. Conventional
processing methods sum (average) the beam covariance matrices over
many snapshots, as shown in FIG. 5A, yielding an eigenvalue
spectrum spreading over many eigenvalues, as shown in FIG. 5B).
For an embodiment of the invention with reference to the flowchart
in FIG. 6 for searching for a target bearing rate at a fixed range,
one assumes a bearing rate .alpha., which yields a
.DELTA..theta.=.alpha..degree., per unit time as shown by the
dashed line in FIG. 3. One searches for a that yields the maximum
eigenvalue for the beam covariance matrix in the target space by
the algorithm described below. For each time frame, the beam
sub-matrix is shifted by an index equal to
.DELTA..theta.=-.alpha..degree. per unit time in Step 70 of FIG. 6.
The resulting matrices are summed or averaged in Step 71. One
determines the largest eigenvalue of the summed covariance matrix
in Step 72. One finds the .alpha..sub.0 that yields the maximum
eigenvalue in Step 73. This value of .alpha..sub.0 should reveal
the target bearing-rate in Step 74. For the true .alpha., the
shifted beam covariance sub-matrix for time t.sub.i should occupy
the same signal beam space as the beam covariance sub-matrix at
t.sub.l, so that they are added up coherently. The entire beam
covariance is then re-processed using .alpha..sub.0 and summed in
Step 74. The summed beam covariance matrix is used to calculate the
MVDR beam power in Step 75.
For illustrative numerical simulations, a bottom-mounted HLA is
considered, the HLA being located in a shallow water environment in
the coast of California where the water depth is 210 m, the sound
speed is close to 1490 m/s for the majority of the water column
except for the top 30 m, and the sound speeds increase to 1525 m/s
at the surface. The HLA shall have, for example, 100 elements
spaced at 6 m uniformly. For the simulated data, the acoustic
signal originates from a fast bearing-changing target and a slow
bearing-changing interference source. The target has a speed of 20
knots moving from -6.degree. to 6.degree. in bearing from the
broadside of the HLA in 100 time frames. The target range is 5 km
and the target depth is 50 m. The interference source is a surface
ship with a radiation source at a depth of 5 m. It is located at a
range of 10 km, traveling with a speed of 5 knots. It changes
bearing form 30.degree. to 33.degree. in the same time period. It
has a source level 20 times stronger than the signal. The
conventional MVDR beam outputs using a white noise constrain of 2
dB is included in FIG. 9, designed as the Before Compensation
figure, for comparison later with the motion compensated result.
The beam at the broadside direction has a much wider width than the
case for a target at a fixed bearing because the signal has covered
a bearing from -6 to 6 degrees.
The data is processed using 1.degree. beam near the broadside
directions. This leads to a beam increment of
.DELTA.=sin(1.degree.).about.0.0174, and hence a total of
2/.DELTA..apprxeq.115 beams in the sin .theta. space (versus
N=100). For the eigenvalue calculations, we shall use a beam
sub-matrix of dimension larger than 5 to include the beam spread
due to multipath arrivals and source bearin change. The eigenvalue
spectrum is calculated for a sub-matrix {circumflex over (Q)} of
dimension 11.times.11 centered on the signal or interference
bearings.
For discrete beams, the search procedure is to re-number the beam
indices of the beam cross-spectral matrix
a.sub.dataa.sub.data.sup.H for each data sample according to a
hypothesized bearing track, as depicted in FIG. 7, and then add
them up to produce a beam covariance matrix. The beam index is
numbered from 1 to 115 with the beam at sin .theta.=-1 as no. 1.
Using FIG. 7 as an example, there is no bearing change for the
first 4 data frames; that is, the signal stays in beam no. 52.
Thus, the (complex) beam covariance matrices for time 1 to 4 are
added together. For the time frames 5-13, the signal bearing has
changed by one beam. The beam cross-spectral matrix for these
(5.sup.th-13.sup.th) time frames will be shifted up by one index
and shifted left by one index with the top-most row and left-most
column wrapped around to the bottom-most row and right-most column.
The resulting (5.sup.th-13.sup.th) beam cross-spectral matrices
will be added to the cross-spectral matrices of the previous four
(1.sup.st-4.sup.th). For the next 9 data frames, according to FIG.
7, the target bearing has changed by two beams. Hence, the beam
cross-spectral matrices will be shifted up and shifted left by two
indices and added to the previous beam cross-spectral matrices.
This process is continued for all 100 data frames for the
hypothesized bearing track of FIG. 7. A final beam covariance
matrix is obtained for the hypothesized bearing track. This beam
covariance matrix will be in principle the same as that for a
stationary source, since in the rotating coordinates, the source is
stationary.
For each hypothesized target-bearing rate (i.e., bearing track),
one finds the largest eigenvalue of the beam covariance sub-matrix
in the signal beam space. After repeating the above process for a
given range of bearing rate (i.e., bearing track), one plots the
level of the first eigenvalue as a function of the search
bearing-rate. The result is shown in FIG. 8. FIG. 8 shows a peak at
an estimated bearing rate of .about.0.1 deg/unit-time, which is
slightly lower than the true value of 0.12 deg/unit-time. The
estimation error is due to the discrete beams used for bearing rate
compensation.
Using the (final) beam covariance matrix obtained at the bearing
rate of .about.0.1 deg/unit-time, the beam domain MVDR, Eq. (7) is
applied, and the output beam power is plotted in the After Motion
Compensation graph of FIG. 9. The signal has a sharp peak as
expected for MVDR. The interference source shows up as a broadband
peak because its motion was not compensated. The
peak-to-interference ratio has improved by 6 dB over the
element-space MVDR as shown in the Before Compensation graph of
FIG. 9, which did not compensate for motion.
The reason for the interference signal suppression when the
interference source has a different bearing rate than the signal is
explained in FIG. 10. Comparing the signal beam covariance matrix
before and after the motion compensation, the beam covariance
sub-matrices of the signal in the signal beam covariance matrix
after motion compensation were grouped together and added up
coherently, whereas the beam covariance sub-matrices of the
interference in the signal beam covariance matrix after motion
compensation were further spread out in the beam space. Thus, the
beam power of the signal is enhanced and the beam power of the
interference is not. The strength of the interference relative to
the target signal is suppressed after motion compensation compared
with that before motion compensation.
The beam domain approach optionally presents an advantage on
interference rejection even for a stationary signal and
interference. In the element space, the largest eigenvalue is
likely to be dominated by a loud interference. In cases when the
signal and interference fields are not orthogonal, as is often the
case in practice, it is difficult to remove the eigenvector of the
interference without losing the signal energy. The situation is
different in the beam domain. Note that in the signal beam
sub-space, the largest eigenvalue will be dominated by the signal,
since energy leakage from the interference source to the signal
beam has been suppressed by the array beamforming peak-to-sidelobe
ratio (.gtoreq.20 dB for the example given above). Removal of the
interference eigenvalue/eigenvector has a lesser effect on the
signal field. Likewise, in the beam sub-space pointing to the
interference, the largest eigenvalue will be dominated by the
interference field.
To investigate the target spectral content, one uses a beam
sub-space scissorgram following the target since the spectra of
individual elements are dominated by the interference signal. For
the same reason, to integrate the signal energy coherently across
the array for a bearing-changing target, one should use the signal
beam covariance matrix following the target. In contrast, the
element space covariance matrix will be dominated by the
interference field as shown above. The beam covariance sub-matrix
at the signal direction has negligible contribution from the
interference field.
Search for Target Range Rate for a Fixed Bearing
Another embodiment of the invention addresses motion compensation
for a fast moving target at a fixed bearing. An illustrative,
numerical example involves a fast range-changing target at the
bearing of 0.degree. with a depth, speed, and initial range same as
in the case considered above. The surface interference is, for
example, at a range of 20 km with a source level 50 times of the
signal. It has a fixed bearing of 30.degree. with the same depth
and speed as described above. A white noise .about.20 dB down from
the signal at the element level is assumed.
For range-rate compensation, one needs a discriminator related to
range that differentiates the target signal from the interference
field. The discriminator to be used here is the frequency-range
(scaling) relationship as predicted by the waveguide invariant
theory. It has been previously shown for a time-reversal vertical
line array ("VLA") that focusing the acoustic energy to a slightly
different range than the original source location can be
accomplished by frequency shifting. Likewise, for matched-field
processing on a VLA, source range change can be compensated for by
frequency shift of the covariance matrix. However, the same
approach does not work for a HLA, as the element space covariance
matrix for a HLA does not have the same frequency and range
dependence as for a VLA. The technical reason is that there is only
one range parameter for a VLA, but there are many range parameters
for a HLA.
The beam covariance matrix for a source changing range will exhibit
the same frequency-range dependence as predicted by the waveguide
invariant theory. Accordingly, source range-change can be
compensated by frequency shift. Consequently, a range compensation
algorithm can be used to search for the target range-rate and
recover the signal loss due to motion. The interference field is
suppressed when the interferer has a different range rate than the
target source.
The beam power at the signal direction, that is, broadside to the
array, is a function of frequency and time can be plotted. The
signal travels 1.03 km during a time period of 100 units. The beam
intensity in such a plot exhibits a striation pattern as a function
of frequency and time. This pattern has been shown previously to be
identical to that of a single element except that the level has
been enhanced by the signal gain.
The intensity of the beam covariance matrix between a beam one
index lower and another beam one index higher than the signal beam
can also be plotted. Such a plot shows the same striation pattern
as the beam power. The beam power relates to the diagonal element
of the beam covariance matrix.
The slope of the above striation is related theoretically to the
so-called waveguide invariant parameter, .beta.. The waveguide
invariant theory says that the slope of the striation for the
single-element acoustic intensity, plotted as a function of
frequency and range, is given by
d.omega.d.beta..times..omega. ##EQU00002## where .beta. is given by
the ratio of the difference of phase slowness between a pair of
modes over that of the group slowness between the same pair of
modes. The parameters .beta. is called the waveguide invariant
since it is a "universal" number for a group of modes. Assuming the
source travels with a constant velocity v, the above equation can
be rewritten as
d.omega.d.beta..times..omega..times..times..ident..gamma.
##EQU00003## where .gamma. is the slope of frequency striation with
respect to time. Based on the analysis above, the waveguide
invariants can be extended to the beam intensity, and the beam
covariance matrix. The parameters .gamma. is related to the range
rate v.
Based on Eq. (9), the beam intensity at the signal direction
satisfies the following equation,
B(.omega.,t+dt)=B(.omega.+.gamma.d.omega.,t). (10) Thus, the signal
range change can be compensated by a frequency-shift between the
adjacent data frames. The same is also true for the elements of the
beam covariance matrix indexed around the signal directions. The
sidelobe beams outside the signal arrival directions will have a
different striation pattern.
The processor starts with a potential target of interest at a given
bearing. The processor need not assume that .beta. is known in
advance. The processor also need not assume that the source range
is known. An approximate value of the .gamma. can be measured from
the frequency striation slope of the intensity spectrum of the
signal beam. The exact value will be searched for by the motion
compensation processor. The parameter .gamma. will be called the
frequency-shift-rate or frequency-rate for short.
An embodiment of the invention is shown by way of example in the
flowchart of FIG. 11 for searching for a target range rate at a
fixed bearing. The algorithm for frequency-rate search shown in
FIG. 11 is described as follows. For a given frequency rate, the
beam covariance matrix for each data frame is shifted in frequency
according to Eq. (10) for all of its elements in Step 101. The beam
covariance matrices are then summed in Step 102. We then calculate
the value of the first (largest) eigenvalue of the beam covariance
sub-matrix at the signal arrival direction. The process is repeated
for other anticipated frequency rates. The eigenvalue is then
plotted as a function of the frequency-shift-rate as shown in FIG.
12. One searches for the largest eigenvalue in FIG. 12, which
yields an estimation of the frequency-rate (0.16 Hz/unit-time in
FIG. 12) associated with the target range rate in Step 103 of FIG.
11. After determining this frequency-rate, the entire beam
covariance matrix will be summed using this frequency-rate in Step
104 of FIG. 11. The final beam covariance matrix will be used by
the beam domain adaptive processor in Step 105 of FIG. 11.
In FIG. 13, the Before Compensation graph shows the beam power
using the element space MVDR algorithm, with the covariance matrix
integrated over the 100 data frames without motion compensation.
The beam pointing to the surface ship is somewhat skewed due to the
spreading of mode arrival angles as remarked above. In FIG. 13, the
After Motion Compensation graph shows the beam power using the beam
domain MVDR algorithm that includes range-rate compensation via the
above frequency-shift algorithm. Comparing the After Motion
Compensation graph with the Before Compensation graph, it can be
seen that the signal-to-interference ratio has improved by 10 dB by
the range-rate compensation algorithm. While the signal power has
been coherently added up following the frequency striation of the
signal, the interference beam power has been suppressed since the
interference field has a different frequency-shift-rate than the
signal. Note that the interferer is at a different range and has a
different speed than the signal source.
Although the above simulation uses a signal at the broadside
direction, the same approach can be applied to a signal at an
endfire direction. It has been shown before that the signal arrival
beams for a near endfire signal have the same beam striation
pattern as the signal beam for a broadside signal. Each signal
arrival beam may have a somewhat lower intensity due to signal
energy spread over multiple beams. Algorithm for Motion
Compensation: Target with a Non-zero Bearing and Range Rate
In another embodiment of the invention, the above processing
techniques can be combined and applied to a target simultaneously
changing bearing and range. Such an embodiment is described, by way
of example, using a flowchart for beam time record compensation for
target motion in FIG. 14. The process described in the flowchart
involves a two-dimensional search for the bearing and range rate.
As discussed above, the first step is to identify a potential
target in the beam time record, and the target beam sub-space. For
a given time window t.sub.i to t.sub.i+N-1, determine a range of
possible bearing-rate from the total bearing change and a range of
possible range-rate that is consistent with the bearing history in
Step 151 of FIG. 14. At each time, shift and wrap around the
elements of the beam covariance matrices according to the
hypothesized bearing-rate in Step 152 and shift the frequency
spectrum according to the hypothesized range-rate in Step 153. Sum
the beam covariance matrices over N data samples in Step 154.
Search for the bearing-rate and range-rate that yield the highest
signal power in Step 155. Use the beam covariance matrix determined
with .alpha..sub.0 and .beta..sub.0 for MVDR beamforming in Step
156. This yields the motion compensated beam power at time t.sub.i.
Proceed to process next batch of data from t.sub.j to
t.sub.j+N-1,j=i+l to i+M.
Depending on the number of beams used, an alternative is to search
.alpha..sub.0 and .beta..sub.0 using only the beam sub-matrices in
the target signal space and then process the entire beam covariance
matrices using .alpha..sub.0 and .beta..sub.0 as depicted in FIGS.
6 and 11.
Obviously, many modifications and variations of the instant
invention are possible in light of the above teachings. It is
therefore to be understood that the scope of the invention should
be determined by referring to the following appended claims.
* * * * *